Certain rigid irregular $G_2$-connections constructed by the 1st-named author are related via pullbacks along a finite covering and Fourier transform to rigid local systems on a punctured projective line. This kind of property was first observed by Katz for hypergeometric connections and used by Sabbah and Yu to compute irregular Hodge filtrations for hypergeometric connections. This strategy can also be applied to the aforementioned $G_2$-connections and we compute jumping indices and dimensions for their irregular Hodge filtrations.

中文翻译：

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刚性 G2 连接的不规则 Hodge 数

由第一作者构建的某些刚性不规则 $G_2$-连接通过沿有限覆盖的回调和傅里叶变换与穿孔射影线上的刚性局部系统相关联。这种性质首先由 Katz 观察到超几何连接，并被 Sabbah 和 Yu 用于计算超几何连接的不规则 Hodge 过滤。这个策略也可以应用到前面提到的$G_2$-connections，我们计算跳跃指数和维度来计算它们的不规则 Hodge 过滤。